Mathematical Modeling

To model real-world situations through mathematical methods and representations and interpret mathematical models and representations, moving across multiple representations, as appropriate to purpose.

POSSIBLE INSIGHTS
Mathematical situations can be represented verbally, numerically, in tables, symbolically, or graphically. One form may be best to interpret or communicate information.

SUGGESTED REFLECTION QUESTIONS

• Which representation is most useful in this situation?
• Which representation can best tell the story of this relationship, pattern, trend, etc?
• Is there a representation that can make the significant relationships more obvious?

Problem Solving

To solve problems using numeric, graphic, algebraic or approximation methods.

POSSIBLE INSIGHTS
Information within a situation helps determine possible strategies to use to systematically reach a solution, although one may be best depending on the situation and tools at hand.

SUGGESTED REFLECTION QUESTIONS

• Is this the most efficient and effective solution, given what I know, what I must assume, and where I am headed?

Descriptive Statistics

To describe and analyze data sets that answer questions about imprecise situations, through strategic use of statistical measures and representations.

POSSIBLE INSIGHTS
Statistical questions can be accurately answered using several statistical descriptors, interpreted in context, including single-number measures of center and variability, and descriptions of shape and other general patterns.

SUGGESTED REFLECTION QUESTIONS

• How can math accurately describe what is typical of a large and diverse group?

Transformations

To reason about attributes and relationships of geometric objects by using transformations.

POSSIBLE INSIGHTS
Transformations can be studied in terms of functions, where the inputs and outputs are points in the plane, rather than numbers.

SUGGESTED REFLECTION QUESTIONS

• How can algebra be a tool for geometric understanding and modeling?
• Which properties remain invariant under this transformation?
• What conjectures can I draw knowing these invariances?